Proof of Bernoulli's Inequality using Mathematical Induction

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The Math Sorcerer

9 жыл бұрын

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Proof of Bernoulli's Inequality using Mathematical Induction

Пікірлер: 36

@melynx1159 Жыл бұрын

I'm so glad this channel exists. Despite my enormous passion for the subject, my maths skills mysteriously vanished during high school and I blame much to the overcomplicated way people teach in my country. This explanation is so easy that even a 6 years old kid could understand it. Thank you so much for allowing me to enjoy maths again! ❤❤❤

@benyoutube234 Жыл бұрын

I have been trying to find out why a>-1 and you are the only one who mentions it so thanks a lot.

@dangdangheather Жыл бұрын

literally the only video with an unknown im so grateful for you thankuuuuu

@TheMathSorcerer Жыл бұрын

😀

@dangdangheather Жыл бұрын

@@TheMathSorcerer :D

@user-nf6rs2rh4u 2 жыл бұрын

Thank you very much for this video. It was really useful to me. 👍🏼

@FadeStrategy 3 жыл бұрын

Thank you so much.

@mantas9827 4 жыл бұрын

Thanks!!

@forthrightgambitia1032 3 жыл бұрын

Nice. From this you can prove a series of inequalities that lead to the famous Gibbs inequality that is important in machine learning (which is why I was here).

@user-li6ev1ro9c 4 жыл бұрын

Dude this is great. Love this vido

@TheMathSorcerer 4 жыл бұрын

Thanks man!

@xJBRRR 7 жыл бұрын

Can you tell me why ka^2 being greater than 0 enables us to drop the term?

@patricksalmas1877 7 жыл бұрын

So what he's basically doing is showing that, (1 + a)^k * (1 + a)^1 >= 1 + (k + 1)a + ka^2 >= 1 + (k + 1)a He never actually drops the ka^2, what he's really doing is saying that since we know ka^2 will be at least zero, we know that 1 + (k + 1)a will always be less than or equal to itself plus that ka^2. Since the we know that (1 + a)^k * (1 + a)^1 >= 1 + (k + 1)a + ka^2 (base on the induction hyp.). And we know that 1 + (k + 1)a + ka^2 >= 1 + (k + 1)a, we can then conclude that (1 + a)^k * (1 + a)^1 >= 1 + (k + 1)a, and that is what needed to be shown.

@davidfair4852 7 жыл бұрын

Awesome, thanks.

@Jazoopi 4 жыл бұрын

@@patricksalmas1877 Godbless

@TheDropdeadZed 4 жыл бұрын

If the LHS is greater than or equal to the RHS when ka^2 is part of the RHS, then the LHS will STILL be greater than or equal to the RHS when we make the RHS a bit smaller (since ka^2 is either 0, or it's a positive number). E.g. if LHS = 20, RHS = 10. We take away ka^2 = 2, so then RHS becomes 8. 20 is still greater than or equal to 8 so the statement is still true. I guess he didn't really 'take away' ka^2 since he didn't subtract it from both sides, essentially he just removed it from the picture since it didn't affect the inequality.

@jimallysonnevado3973 3 жыл бұрын

as an example 3+5>3 because 5 is positive we didnt really drop the 5 here

@TheMathSorcerer 9 жыл бұрын

@ejsimon813 9 жыл бұрын

thank you

@shuvammitra8700 Жыл бұрын

Thank you so much

@chrysanthcrest 7 жыл бұрын

Thank you!

@TheMathSorcerer 7 жыл бұрын

@bauyrzhankurmangaliyev347 3 жыл бұрын

why it is not a>-1?

@iRealmath 3 жыл бұрын

Some time ago I saw an article where a>-1 is taken instead of a=>-1. So I guess this guy had a mistake. (sorry for my English)

@dragon-7511 2 жыл бұрын

a is greater than -1 .why used ≥ this sign

@somiechannel7407 2 жыл бұрын

❤️❤️❤️

@Medodell 3 жыл бұрын

I see you used the theorem to prove it, I really do not get it

@Copryon 2 ай бұрын

absolute chad

@awesomecraftstudio 10 ай бұрын

gotta love this shit

@DarkOutsideNow 4 жыл бұрын

Thank you for the video!!... Math: formulas written by people who are lazy, so they short handed everything into hard-to-understand formatting that requires formal education. Sometimes without knowing what level or type of math that's applied, it becomes hard to provide the answer. Suppose x + y = (x+y) is true. prove it. AHH!! Which way?!?! Elementary school style (count those apple, oranges, which are all fruits) or advanced math using proofs that take 10x longer? (Edit for slight grammar issue)

@isaactaremwa001 4 жыл бұрын

Not so clear but thanks

@oneaboveall6239 4 жыл бұрын

well i understand Bernoulli's Inequality but i still hate pure math

@energy-tunes Жыл бұрын

where numbers

@maxpercer7119 2 жыл бұрын

gets a little murky the logic dealing with the sign of (1+a ) at 3:45 , kind of reverse logic. see math.stackexchange.com/questions/181702/proof-by-induction-of-bernoullis-inequality-1xn-ge-1nx Nice video, i am hooked to math (and your videos).